ABSTRACT
Polynomials and rational functions are Maple's favourite data types. This chapter looks at their arithmetical properties, which resemble those of integers and rationals, respectively. Arithmetically, polynomials behave much like integers. The formula for polynomial multiplication is a bit more complicated than that for addition. The chapter considers polynomials whose coefficients are numbers. However, all that is required from the coefficients is the possibility of performing the arithmetical operations of sum, subtraction, and multiplication. These properties are enjoyed by polynomials, so it makes sense to consider polynomials whose coefficients are themselves polynomials. The lack of closure of the integers under division led to the introduction of the rational numbers. The decomposition into partial fractions is an important representation of a rational function. By contrast, the function factor, when applied to a rational expression, provides a simplified and fully factored form, and may be used as an alternative to simplify, keeping in mind that it is more expensive to evaluate.
